 
Summary: Optimization and Optimal Control, pp. 128
P.M. Pardalos, I. Tsevendorj, and R. Enkhbat, Editors
c 2003 World Scientic Publishing Co.
Extragradient approach to solution of two person
nonzero sum games
Anatoly Antipin (antipin@ccas.ru)
Computing Center of Russian Academy of Sciences,
Vavilov str., 40, 119991 Moscow, Russia
Abstract. The two person nonzero sum game is considered in the following
statements: in classical form, under the availability of inequalityconstraints and
coupled constraints. A extragradient method for computing Nash equilibria for
these statements is suggested and its convergence is investigated.
Keywords: Nonzero sum game, extragradient method, coupled constraints,
convergence.
1 Introduction
Let = X1 × X2 be a rectangle, where X1 Rn1
1 , X2 Rn2
2 are convex closed sets
from nitedimensional Euclidean spaces, generally speaking, various dimensionality.
Let functions f1(x1, x2) + 1(x1), f2(x1, x2) + 2(x2) be determined on the product
